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flysun: ½ð±Ò+5, ¡ï¡ï¡ï¡ï¡ï×î¼Ñ´ð°¸ 2013-07-27 08:12:34
Ó¦¸ÃÊÇ0£¬ÒòΪÔÚx -> 0ʱ£¬ Õ¹¿ª sinh(x)=x+1/6*x^3+1/120*x^5+O(x^6), cosh(x)=1+1/2*x^2+1/24*x^4+O(x^6)£¬ËùÒÔ y=(sinh(x)-x)/(cosh(x)-1) ¡Ö 1/6*x^3/ (1/2*x^2)= 1/3 x -> 0¡£
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½«sinh(x)ºÍcosh(x)·Ö±ðTaylorÕ¹¿ª£¬¿ÉÒÔ·¢ÏÖsinh(x)-x = x^3/3!+x^5/5!+...; ¶øcosh(x)-1 = x^2/2!+x^4/4!+...;
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cosh(x)= (e^x+e^{-x})/2,
sinh(x)= (e^x-e^{-x})/2,
d(cosh(x))/dx = sinh(x), d(sinh(x))/dx =cosh(x)

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y= ( cosh(x)-1) / sinh(x) ÔÙÀ´Ò»´Î¸Ã·¨Ôò£¬
= sinh(x) / cosh(x)  ÏÖÔÚÊÇÕý³£º¯ÊýÖµ
=0.

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cosh(x)=1+ x^2/ 2! + x^4/ 4! +...
sinh(x)= x + x^3/ 3! + x^5 / 5! +...
ËùÒÔÔÚÁãµã¸½½ü y(x) = x/3 + o(x).
We_must_know. We_will_know.
4Â¥2013-07-26 13:43:23
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ʹÓÃÁ½´ÎÂޱȴ﷨Ôò¾ÍÄÜÇó³öÀ´µÄ, ½á¹ûÊÇÁã. ºÜ¼òµ¥µÄ°¡.
Themorewedo,themorewecando.
7Â¥2013-07-27 06:16:13
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